Pendulum Experiment?

Question

When experimenting with pendulums, I began wondering about several things. First of all, we were required to obtain a string and make a loop 40 cm from the top tip. After 20 seconds we were to measure the number of swings, and then perform the same experiment three times for string with a length of 80 cm and 120 cm. Is it correct that as the length of the string increased, the number of swings decreased? Why is this so? Will adding more weight to the string make a noticeable difference? Dividing the average number of swings per length of string after testing 3 times by 20(seconds) produced larger numbers than when dividing the average number of swings for the shorter string. Would that not mean that the linger the string on the pendulum, the more swings? Unfortunately I could not find a source to explain this, and I would hope that certain individuals with knowledge about this experiment could shed some light. Many thanks!

Answer 1

The period of a pendulum is 2*pi*sqrt(l/g), where l is the length and g is the graviational acceleration. The period is the time it takes for the pendulum to swing and return to its original position, and as you can see, it increases with the square root of length. Thus, a longer pendulum has a longer period, and therefore completes fewer swings in a given timeframe. The period of a pendulum is not affected by the amount of mass on the string. However, if you put a pendulum on the Moon, where there is about 1/6 the gravity of Earth, it would increase its period by a factor of roughly 2.5.

Answer 2

The laws governing the motion of a pendullum are NOT approximate. I can't remember the exact derivation of the commonly used pendulum equations for period, versus mass, versus length, but there may be some approximations to keep the equations simple (i.e. small angle - if I recall then sin(theta)=theta...) but the exact differential equations can be used if the simple formulae are insufficient. There are a lot of variables; The accuracy of your results is completely dependent on the accuracy of your experiment... Things which have error: -Your timing measument -Air resistance (run pendulum in a vacuum if possible) -Your mass measurement -Your length measument -Friction at the attached end of the pendulum -Earth's gravitational constant (varies by location) -Tidal effects (the moon) I'm sure there are more...

Answer 3

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